GRMHD Simulations of Jet Formation with Newly-Developed GRMHD Code

1. GRMHD Simulations of Jet Formation with Newly-Developed GRMHD Code K.-I. Nishikawa (NSSTC/UAH), Y. Mizuno (NSSTC/MSFC/NPP), P. Hardee (UA), S. Koide (Kumamoto Univ.), G.J. Fishman (NSSTC/MSFC) Reference: Mizuno et al. 2006, in preparation

2. Introduction M87 • Astrophysical jet is a outflow of highly collimated plasma gas • In Microquasar、Active Galactic Nuclei、Gamma-Ray Bursts, Jet velocity is nearly light velocity（～c）. • Compact object（White Dwarf、Neutron Star、Black Hole）+Accretion Disk system • Problem of Astrophysical Jet • Acceleration mechanism • Collimation • Long term stationality • Model of Astrophysical Jet • Most confidential model is magnetohydrodynamic model

3. Propose to make a new GRMHD code • The Koide’s GRMHD Code (Koide 2003) has been applied to many high-energy astrophysical phenomena and showed pioneering results. • However, the code can not perform calculation in highly relativistic (g>5) or highly magnetized regimes. • The critical problem of the Koide’s GRMHD code is the schemes can not guarantee to maintain divergence free magnetic field. • In order to improve these numerical difficulties, we have developed a new 3D GRMHD code RAISHIN(RelAtIviStic magnetoHydrodynamc sImulatioN, RAISHIN is the Japanese ancient god of lightening).

4. Detail of Schemes • Use conservative schemes to solve the 3D GRMHD equations in each spatial direction * Reconstruction • Piecewise linear method (Minmod and MC slope-limiter function; second-order), convex ENO (third-order), Piecewise parabolic method (fourth-order) * Riemann solver • HLL approximate Riemann solver * Constrained Transport • Flux interpolated constrained transport scheme * Time advance • Multi-step TVD Runge-Kutta method (second and third -order) * Recovery step • Koide 2 variable method and Noble 2D method

5. Flexibility of a New GRMHD code • Multi-dimension (1D, 2D, 3D) • Special and General relativity • Different boundary conditions • Different coordinates (RMHD: Cartesian, Cylindrical, Spherical and GRMHD: Boyer-Lindquist of non-rotating or rotating BH) • Different spatial reconstruction algorithms • Different time advance algorithms • Different recovery schemes

6. Linear Alfven wave Propagation Tests • Calculate the L1 norm of the difference between the final state and the initial state • All reconstruction schemes show the second-order of convergence L1 norm of the error in density

7. Relativistic MHD Shock-Tube Tests Balsara Test1 (Relativistic version of Brio & Wu) • The results show the good agreement of the exact solution calculated by Giacommazo & Rezzolla (2005). • Minmod slope-limiter and CENO reconstructions are more diffusive than the MC slope-limiter and PPM reconstructions. • Although MC slope limiter and PPM reconstructions can resolve the discontinuities sharply, some small oscillations are seen at the discontinuities. Black: exact solution, Blue: MC-limiter, Light blue: minmod-limiter, Orange: CENO, red: PPM

8. 2D GRMHD Simulation of Jet Formation • Initial condition • Geometrically thin accretion disk (rd/rc=100) rotates around a black hole (a=0.0, 0.95) • The back ground corona is free-falling to a black hole (Bondi solution) • The global vertical magnetic field (Wald solution; B0=0.1 , 0.05(r0c2)1/2) • Numerical Region and Mesh points • 1.0 rS< r < 40 rS, 0< q < p/2, with 128*128 mesh points • Method • minmod slope-limiter, HLL, flux-CT, RK3, Noble 2D method

9. Results Color: density (upper), plasma beta (lower) White curves: magnetic field lines (upper), toroidal magnetic field (lower) vector: poloidal velocity • The simulation results show that the jet is formed in the same manner as in previous work (Koide et al. 2000) and propagates outward. • In the rotating black hole cases, jets form much closer to the black hole’s ergosphere and the magnetic field is strongly twisted due the frame-dragging effect.

10. Summary • We have developed new 3D GRMHD code by using a conservative, shock-capturing scheme. • The numerical fluxes are calculated HLL aproximate Riemann solver method • Flux-interpolated CT scheme is used to maintain a divergence-free magnetic field • We have discribed code perfomance on various 1 dimensional special relativistic test problems and they show accurate results • We have performed the jet formations from a geometirically thin accretion disk near non-rotating and rotating black holes. • The simulation result showed the jet formation by the same manner of previous works and propagate longer time than previous GRMHD simulations.

11. Future Work • Code development • Parallelization by using MPI (speed up) • Physical EOS • Neutrino treatment (cooling, heating) • resistivity • Connection to relativistic radiation transfer (observational expectation); see Nishikawa et al. 2005 (astro-ph/ 0509601) • Connection to Nucleosysthesis • Apply to many high-energy astrophysical phenomena (especially relativistic outflows from AGNs, microquasars, neutron stars, and GRBs and related physics)